few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Standard options: 
A. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


Thought: This task asks students to compare two fractions that are equal. The two fractions have different numerators and denominators (e.g. 1/4 and 3/12). The students need to explain why the two fractions are equal by drawing a picture, which involves using visual fraction models.
Answer: A, B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_000212

4
options: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
problem_activity: Warm-up
In this warm-up, students revisit quadratic expressions in different forms and what the expressions reveal about the graphs that represent them. They match equations and graphs representing two quadratic functions. The axes of the graphs are unlabeled, so students need to reason abstractly about the parameters in the expressions and the features of the graphs.
Student Facing
[IMG]
Here are graphs representing the functions
\(f\)
and
\(g\)
, given by
\(f(x) = x(x+6)\)
and
\(g(x) = x(x+6)+4\)
.
Which graph represents each function? Explain how you know.
Where does the graph of
\(f\)
meet the
\(x\)
-axis? Explain how you know.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Invite students to share their matches and explanations. If one or more explanations in the Student Response are not mentioned, bring them up so that students can see multiple ways of reasoning about the equations and graphs.


correct_option_index: 0

1

2